On the first negative Hecke eigenvalue of an automorphic representation of GL2(AQ)

• 作者: Yuk-Kam Lau Ming Ho Ng Hengcai Tang Yingnan Wang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（11）
• 所属期刊栏目: Articles
• 页码范围: 2381-2394
• 页数: 14页
• 语种: 英文

摘要

Let π be a self-dual irreducible cuspidal automorphic representation of GL2 (AQ) with trivial central character.Its Hecke eigenvalue λπ(n) is a real multiplicative function in n.We show that λπ(n) ＜ 0 for some n ＜＜ Q2/5π,where Qπ denotes (a special value of) the analytic conductor.The value 2/5 is the first explicit exponent for Hecke-Maass newforms.